research article distortion optimization of engine...

Research ArticleDistortion Optimization of Engine Cylinder Liner UsingSpectrum Characterization and Parametric Analysis

Zhaohui Yang,1 Baotong Li,2 and Tianxiang Yu1

1School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China2State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Correspondence should be addressed to Baotong Li; [email protected]

Received 19 January 2016; Accepted 13 April 2016

Academic Editor: Xiangyu Meng

Copyright © 2016 Zhaohui Yang et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In an automotive powertrain system, the cylinder liner is one of themost critical componentswhich possesses the intricate structuralconfigurations coupled with complex pattern of various operational loads. This paper attempts to develop a concrete and practicalprocedure for the optimization of cylinder liner distortion for achieving future requirements regarding exhaust emissions, fueleconomy, and oil consumptions. First, numerical calculation based on finite element method (FEM) and computational fluiddynamics (CFD) is performed to capture the mechanism of cylinder liner distortion under actual engine operation conditions.Then, a spectrum analysis approach is developed to describe the distribution characteristic of operational loads (thermal andmechanical) around the circumference of a distorted cylinder bore profile; the FFTprocedure provides an efficientway to implementthis calculation. With this approach, a relationship between the dominant order of distortion and special operational load isobtained; the design features which are critically relative to cylinder liner distortion are also identified through spectrum analysis.After characterizing the variation tendency of each dominant order of distortion through parametric analysis, a new design schemeis established to implement the distortion optimization. Simulation results indicate that a much better solution is obtained by usingthe proposed scheme.

1. Introduction

In an automotive powertrain system, the cylinder liner isone of the most critical components affecting the operationalperformance of an engine. With the ever-increasing demandin higher efficiency of engine sealing units which involvesboth oil consumption and exhaust emission, the demand onimproved tightness of contact on piston ring/cylinder linerinterface (PRCI) is also increasing [1–3]. In addition, lowerfriction design is also being aggressively pursued for thetribological system (e.g., piston ring/cylinder liner) whichis important for a better fuel economy [4–6]. However, theformer demand (i.e., sealing efficiency) requires a higher pre-tightening force on piston ring which will lead to excessiveengine friction losses and subsequently, resulting in an adverseeffect on the fuel consumption. Therefore, higher sealingefficiency and lower engine friction losses are two conflictinggoals. In this regard, cautions should be placed in the qualityof the interface between piston ring and cylinder liner [7].

Due to imperfections in manufacturing and pretighteningprocess, as well as complex pattern of various operationalloads, an ideal circular cylinder bore cannot be achieved dur-ing engine operation process. Hence, the elastic piston ringshould conform to the distorted cylinder bore. However, ifsuch distortions become too large, the piston ring may beunable to fully conform to the cylinder bore, and this imper-fection may influence the normal engine operation in termsof increasing component friction, wear, and oil consumption.To this end, the piston rings may achieve better sealingcharacteristics within a low distorted cylinder bore, and, forunchanged sealing demand, the engine friction losses couldbe reduced by decreasing the pretightening force on pistonrings. That is, a low distorted cylinder liner opens up poten-tials for resolving the above conflict.

The ability to predict and optimize the geometrical dis-tortions of cylinder liner has generated significant interest inrecent years. Many analytical and computational tools havebeen used to attack this problem. A pioneering analytical

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016, Article ID 9212613, 11 pageshttp://dx.doi.org/10.1155/2016/9212613

2 Mathematical Problems in Engineering

work dealing with the presentation of a distorted cylinderbore profile was performed byGintsburg [8]. In this work, thesealing characteristic of a splitless piston ring was analyzedby approximating distortions from the ideal circular shapewith a Fourier series. By describing a distorted bore profile inthis form, Mueller [9] further developed a set of bounds foreach Fourier order of distortion, and Luenne and Ziemb [10]adopted these bounds in the development of a measurementsystem for evaluating the distortion characteristics of cylin-der liner. Similarly, Dunaevsky [11, 12] explored a randomprocess based scheme to present the tightness of contact onPRCI. In this scheme, a design criterion was proposed toquantify amplitude and order of bore distortions regardingthe piston ring conformability. Although these studies enablecomplex bore geometries to be decomposed into a seriesof simpler distortion orders, the distribution characteristicof operational loads (thermal and mechanical) around thecircumference of a distorted cylinder bore profile was notyet to be fully analyzed. A systematic approach focusing onthe relationship between each Fourier order of distortionand various operational loads was not given, though thisrelationship may be utilized to get a better understanding forthe mechanical nature of cylinder liner distortions.

As a different approach, the numerical simulation basedon finite element method (FEM) is very useful to predictthe three-dimensional distortions of cylinder liner. Theseapproaches take into account pretightening force, heat trans-fer, and complicated combustion process which the aboveanalytical models neglect. Soua et al. [13] proposed a classicalFE model of engine structure to deal with the computationof cylinder liner distortions. However, this model was exces-sively simplified by using the symmetry assumptions. In fact,Maassen et al. [14] experimentally observed that both thestress fields and distortion patterns on cylinder liner are bynomeans axis-symmetric and rotational symmetric.With thedevelopment of 64-digit computers and refined calculationtechnique, several studies [15–19] further complemented thefull three-dimensional FE model and simulate the physicalbehavior to evaluate the structural integrity of differentdesign schemes. Although realistic distortions can be pre-cisely captured at any interest point of cylinder liner in thesestudies, some critical issues for distortion optimization alsoremain. For instance, keeping the amplitude of the integraldistortion to be the minimum does not always guaranteethe best solution in the cylinder liner design. Actually, suchintegral distortion has long been considered as a compositeof various orders of bore distortions, and different ordersare sensitive to different operational loads. To truly optimizea design, detailed information for the dominant order ofdistortion is very important.

In summary, the following factors are vital to the successof distortion optimization:

(i) Precise prediction of the distortion patterns on cylin-der liner.

(ii) Clarification of the relationship between each Fourierorder of distortion and various operational loads.

(iii) Parameter characterization of design features whichare critically relative to cylinder liner distortions.

In the scope of this paper, integration of the above statedfactors enables reasonable evaluation of distortion patterns atthe beginning.Then, information from an extensive rating ofspectrum characteristic of bore distortions and operationalloads can be utilized to identify the critical design features.Based on this, the parametric analysis is performed to obtainthe variation tendency of each dominant order of distortion,and optimal design scheme can be achieved based on thesefindings.

2. Computational Model

To establish the analytical methodology of the distortionmechanism of cylinder liner, a line style gasoline engine,having 4 cylinders and 4 strokes, is adopted in this paper. Aprecise structural analysis with appropriate boundary condi-tions is of critical importance for the prediction of realisticdistortions on cylinder liner. The first phase is to definethe complex structural configurations of engine components.Figure 1 shows the FE model of the cylinder structure andwater jacket. Since high temperature and stress gradientsare anticipated in and around the bridge area of both thewater jacket and cylinder structure, these sensitive regions aremeshed with high resolution (i.e., the element aspect ratio isapproximately 2.0) to precisely capture the physical behaviorsoccurred on the solid-fluid interface.The total numbers of theelements and nodes in the model are 601 736 and 690 912,respectively.Thematerial properties of the components takenfrom literature [20] are utilized in this analysis.

Because the distortion of cylinder liner is mainly causedby the thermal stress, the primary target of distortion analysisis to accurately predict the temperature distribution withincylinder structure. The thermal load of cylinder structure ismainly contributed by the heat flux from combustion gasto the cylinder wall. In an operating circle of engine, thetime-averaged heat flux transferred to the cylinder wall fromcombustion gas could be calculated as follows:

𝑞𝑚=1

𝑡0

∫

𝑡0

0

𝛼gas-wall𝑇gas𝑑𝑡 − 𝑇wall1

𝑡0

∫

𝑡0

0

𝛼gas-wall𝑑𝑡, (1)

where 𝑞𝑚is the time-averaged heat flux (W/m2), 𝑡

0is the

operating circle time (s), 𝛼gas-wall is the instantaneous heattransfer coefficient between the combustion gas and thecylinder wall W/(m2⋅K), and 𝑇gas and 𝑇wall represent theinstantaneous temperature of the combustion gas and thecylinder wall (K), respectively.

Among the empirical models [21–23] for calculating theinstantaneous heat transfer coefficient 𝛼gas-wall, Woschni’sformula [24] is considered as the most suitable model for thegasoline engine, which is represented as follows:

𝛼gas-wall = 130

⋅ 𝐷−0.2

𝑝0.8

𝑇−0.53

[𝑏V𝑚+𝑐 (𝑉𝑠𝑇𝑟/𝑃V𝑉V)

(𝑝 − 𝑝0)

]

0.8

,

(2)

where 𝐷 is the cylinder diameter (m), 𝑝 is the instantaneouspressure in the cylinder (MPa), 𝑇 is the instantaneous tem-perature of the combustion gas (K), V

𝑚is the time-averaged

Mathematical Problems in Engineering 3

Cylinder block/liner

Cylinder head

Coolant (cylinder block)

Coolant (cylinder head)

Sub-FE model (fluid part) Sub-FE model (solid part) Complete FE model

Figure 1: FE modeling process of engine components for the structural analysis.

speed of the piston (m/s), 𝑏 is the empirical parameter (forthe intake and exhaust strokes, 𝑏 = 7.14; for the strokes ofcompressing, burning and expanding, 𝑏 = 2.99), and 𝑐 isanother empirical parameter (for the strokes of compressing,intake, and exhaust, 𝑐 = 0; for the process of burning andexpanding, 𝑐 = 3.24𝑒 − 3).

It is necessary to determine the instantaneous pressureand temperature for the solving of the time-averaged heatflux by employing (1) and (2). In this paper, the combustionconditions including pressure and temperature are obtainedthrough the simulation of the operational process by usingKIVA3 program; for calculation details, see literature [24].

Besides the thermal boundary conditions, a modifiedRNG 𝑘-𝜀 turbulent model [25] is employed to simulatethe turbulent flow within the water jacket. Meanwhile, todescribe the pretightening effect on cylinder liner distortion,a required compressive axial load (22KN) is imposed on thebolt bodies, and the contact elements are applied on theinterfaces between cylinder structures, bolts, and gasket.

3. Spectrum Characterization of BoreDistortions and Operational Loads

The interactions between structural mechanics, heat transfer,and fluid coolant are simulated through the FLOTRANcalculationmodule available inANSYS�.The calculation dataspecifies a computational grid and a distortion vector associ-ated with each element node.The grid itself is divided into 73hierarchies, each hierarchy having approximately 256 points.To visualize these data, the amplitude of each distortionvector is mapping onto the computational grid by using thedefault linear interpolation in MATLAB. Figure 2 shows thedistortion patterns on the inner surface of different cylinderliners under hot firing operation condition.

Due to the small structural stiffness in the front and rearside of cylinder structure, the distortion levels of the 1st- and

the 4th-cylinder liner are slightly higher than those of others.The maximum distortion of the 1st-cylinder liner (52.6 𝜇m)is located at the left side (180∘ from 𝑃

𝑠) of the bottom region.

In contrast, themaximum distortion of the 4th-cylinder liner(51.4 𝜇m) is located at the right side (0∘ from𝑃

𝑠) of the bottom

region. As for the 2nd- and 3rd-cylinder liner, the distortionamplitude increases to the maximum value (47.6 𝜇m and48.1 𝜇m) almost 40mm away from the reference point (𝑃

𝑠)

and then diminishes gradually. Noting that the radius of thecylinder bore is 41.5mm, the maximum distortion representsless than 0.27% of the bore radius.

In order to get a deep insight about the mechanism ofcylinder liner distortion under actual engine operation con-ditions, the Fourier analysis used to describe the distortedbore profile [8, 9, 11] is extended in this paper to deal withthe spectrum calculation of various operational loads, suchas thermal load (temperature effect) and mechanical load(pretightening effect). By imposing a polar coordinate system(𝜑, 𝑟), the axis of which coincides with the center of the idealcircular bore profile, the distorted cylinder liner correspond-ing to various orders of bore distortions and operational loadscan bemathematically expressed by the polar radius 𝜉

𝑗(𝜑) and

polar angle 𝜑, which can be written as follows:

𝜉𝑗(𝜑) = 𝑟

𝑗0+

𝑁

∑

𝜔=1

𝑎𝜔cos (𝜔𝜑) + 𝑏

𝜔sin (𝜔𝜑)

(𝑗 = 1, 2, 3) ,

(3)

where 𝜉𝑗(𝜑) (𝑗 = 1, 2, 3) is the circumferential distribution

of distortion, temperature, and pretightening stress, respec-tively; 𝑟

𝑗0(𝑗 = 1, 2, 3) is the nominal radius of the studied

profile (in this paper, for distortion analysis, 𝑟10= 41.5mm,

for thermal load analysis, 𝑟20

= 400K, and for mechanicalload analysis, 𝑟

30= 80MPa,); 𝜔 is the Fourier order number;

𝑁 is the total number of the Fourier orders; 𝑎𝜔and 𝑏𝜔are


060

120180240300360

Ang

le fr

omPs

(∘)

060

120180240300360

Ang

le fr

omPs

(∘)

060

120180240300360

Ang

le fr

omPs

(∘)

060

120180240300360

Ang

le fr

omPs

(∘)

0mm

132mm

180∘ 0∘

90∘

270∘

(360∘)

Ps

Ps

−14.2−5.13.512.320.930.139.248.1

(𝜇m

)

−18.4−8.72.812.522.332.142.452.6

(𝜇m

)

−15.2−6.32.411.220.329.538.747.6

(𝜇m

)

−18.5−8.81.311.120.931.241.651.4

(𝜇m

)

y

z x

y z

x

0 20 40 60 80 100 120 132Distance from Ps (mm)




Cylinder_3 (distortion patterns)



Cylinder_2 (distortion patterns)Cylinder liner (top veiw)

Cylinder liner (front veiw)

Maximum

Maximum

Maximum

Maximum

Maximum

Figure 2: Distortion patterns on the inner surface of different cylinder liners.

the coefficients giving amplitude and phase for each Fourierorder.

During the analysis, the boundary of the studied profile(distortion, temperature, and pretightening stress) is consid-ered to be circumnavigated within a certain plane at constantspeed. The size of the calculation step is determined suchthat one circumnavigation takes time 2𝜋 and the numberof calculation steps is 2𝜔; for instance, 26 = 64 steps areadopted in this research.Hence, the above stated function canbe expressed alternatively in the following form:

𝑥𝑗𝑚

+ 𝑖𝑦𝑗𝑚

= 𝑟𝑗0+

+64/2

∑

𝜔=−64/2+1

(𝑎𝜔+ 𝑖𝑏𝜔)

⋅ [cos(2𝜋𝜔𝑚𝑀

) + 𝑖 sin(2𝜋𝜔𝑚𝑀

)]

(𝑗 = 1, 2, 3) ,

(4)

where 𝑥𝑗and 𝑦

𝑗(𝑗 = 1, 2, 3) are the coordinates describing

the circumferential distribution of distortion, temperature,and pretightening stress, respectively; 𝑚 and 𝑀 are theindex number and total number of the FE data points oneach hierarchy, respectively. The number of calculation stepsselected dictates the number of distortion orders obtainedfrom the Fourier analysis and therefore the level of detaildescribed. Since there are 256 FE data points on each hierar-chy, the 64-point fast Fourier transformation (FFT) enables toprovide enough accuracy for the calculation. Figure 3 showsthe spectrum distribution of distortion patterns on cylinderliner, and the evolution procedure of the dominant order ofdistortion is also given in Figure 4.

It is evident in Figure 3 that the 2nd- and 4th-Fourierorders are the dominant distortion orders. Additionally, the

3rd-, 6th-, and 8th-Fourier orders also contribute to the cylin-der liner distortion in some extent. The evolution procedureshows that the 2nd order of distortion reaches maximumalmost 40mm away from 𝑃

𝑠, and the corresponding value of

the 4th order of distortion is observed at the axial location of20mm.

To clarify the factors causing the dominant order of dis-tortion, the statistical nature of different operational loads isinvestigated by using Fourier analytical model. Figures 5 and6 demonstrate the spectrum distribution of the temperatureand pretightening stress, respectively. It is clear that the 2nd-Fourier order of temperature patterns makes the greatestcontribution to the thermal effect within cylinder liner, whilethe 4th-Fourier order is the most significant term for themechanical effect (pretightening stress).

By comparing the dominant orders of distortions andoperational loads, it can be found that the 2nd order of cylin-der liner distortion is the most sensitive to the thermal loadand the mechanical load (pretightening force) is the mostinfluential factor for the 4th order of distortion.

According to the results fromprevious literatures, the 2ndorder of distortion reflects the ovality of the distorted boreprofile, and the 4th order of distortion represents a clover leafshape. In other words, excessive or inadequate cooling of thecylinder structure may cause thermal expansion differencesaround the circumference of cylinder bore profile whichwill lead to an oval distorted liner shape. Although the 2ndorder of distortion is larger than the distortion caused by thepretightening force, it is difficult for piston ring to conform tothe clover distorted liner shape (4th order of distortion).Thisis probably due to the curvature of the 4th-order bore profilebecomes greater than that of the 2nd-order bore profile.Conclusively, the core of keeping a low distorted cylinderliner is the optimization of the dominant order of distortion,


Cylinder_3 (FFT_Distortion) Cylinder_4 (FFT_Distortion)

Cylinder_2 (FFT_Distortion)Cylinder_1 (FFT_Distortion)

0

20

40

60

80

100

120132

1 2 3 4 5 6 7 8 9 10

Dist

ance

from

Ps

(mm

)

Fourier orders (𝜔)

0

20

40

60

80

100

120132

1 2 3 4 5 6 7 8 9 10

Dist

ance

from

Ps

(mm

)


0

20

40

60

80

100

120132

1 2 3 4 5 6 7 8 9 10

Dist

ance

from

Ps

(mm

)


0

20

40

60

80

100

120132

1 2 3 4 5 6 7 8 9 10

Dist

ance

from

Ps

(mm

)


−6.0

−3.1

−0.2

2.9

5.8

8.8

11.9

14.9

A1𝜔

(𝜇m

)

−5.9

−2.7

0.4

3.5

6.5

9.6

12.8

15.7

A1𝜔

(𝜇m

)

−5.7

−2.8

0.1

3.1

6.0

8.9

11.9

14.8

A1𝜔

(𝜇m

)

−6.3

−3.1

0.2

3.4

6.5

9.2

12.4

15.3

(𝜇m

)

Dominant order (2nd and 4th order)

Dominant order (2nd and 4th order) Dominant order (2nd and 4th order)

Dominant order (2nd and 4th order)

Figure 3: Spectrum distribution of distortion patterns on cylinder liner (𝐴1𝜔).

Maximum Maximum

1st cylinder2nd cylinder

3rd cylinder4th cylinder



0 60 8020 40 120 132100Distance from Ps (mm)

0 60 8020 40 120 132100Distance from Ps (mm)

−1012345678

The 4

th o

rder

of d

istor

tion

(𝜇m

)

−202468

1012141618

The 2

nd o

rder

of d

istor

tion

(𝜇m

)

Figure 4: Evolution procedure of the dominant order of distortion.

which mostly ties in selecting the optimum cooling and pre-tightening parameters for engine operation.Therefore, a pro-per design scheme for water jacket and pretightening processis required to reduce such distortion.

4. Distortion Optimization Based onParametric Analysis

To provide insight on the improvement potential of the mod-ification in water jacket and pretightening process, the para-metric analysis is used to study how the design parameterchanges affect the resulting of cylinder liner distortion. In this

study, the key parameters are denoted by specific symbols,shown as Figure 7. The upper and lower limits of these sym-bols are enumerated below:

𝑃1: (thickness of thewater jacket, initial value is 7mm)

this factor may vary from 5mm to 13mm,

𝑃2: (diameter of the coolant inlet, initial value is

26.8mm) variations within 15% of its initial value arepermitted,

𝑃3: (height of the coolant inlet, initial value is 25mm)

this factor may vary from 25mm to 65mm,


0

20

40

60

80

100

120132

1 2 3 4 5 6 7 8 9 10

Cylinder_3 (FFT_Temperature) Cylinder_4 (FFT_Temperature)

Cylinder_1 (FFT_Temperature) Cylinder_2 (FFT_Temperature)

Dist

ance

from

Ps

(mm

)


0

20

40

60

80

100

120132

1 2 3 4 5 6 7 8 9 10

Dist

ance

from

Ps

(mm

)


0

20

40

60

80

100

120132

1 2 3 4 5 6 7 8 9 10

Dist

ance

from

Ps

(mm

)


0

20

40

60

80

100

120132

1 2 3 4 5 6 7 8 9 10

Dist

ance

from

Ps

(mm

)


Dominant order (2nd order)Dominant order (2nd order)

Dominant order (2nd order) Dominant order (2nd order)

300320340360380400420440

A2𝜔

(K)

300320340360380400420440

(K)

300320340360380400420440

A2𝜔

(K)

300320340360380400420440

A2𝜔

(K)

Figure 5: Spectrum distribution of temperature patterns on cylinder liner (𝐴2𝜔).

66.523

75.507

87.896

94.015

103.625

115.507

64.35474.782

85.101

94.917

105.026

116.189

63.22773.201

83.986

92.963

103.102

112.899

64.52874.645

86.967

95.122

104.807

117.016

020406080

100120132

020406080

100120132

020406080

100120132

020406080

100120132

1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 101 2 3 4 5 6 7 8 9 10

Cylinder_3 (FFT_Pretightening stress) Cylinder_4 (FFT_Pretightening stress)

Cylinder_1 (FFT_Pretightening stress) Cylinder_2 (FFT_Pretightening stress)

Dist

ance

from

Ps

(mm

)

Dist

ance

from

Ps

(mm

)D

istan

ce fr

omPs

(mm

)

Dist

ance

from

Ps

(mm

)

Fourier orders (𝜔) Fourier orders (𝜔)

Fourier orders (𝜔)Fourier orders (𝜔)

A3𝜔

(MPa

)A

3𝜔

(MPa

)

A3𝜔

(MPa

)A

3𝜔

(MPa

)

Dominant order (4th order)

Dominant order (4th order) Dominant order (4th order)

Dominant order (4th order)

Figure 6: Spectrum distribution of pretightening stress patterns on cylinder liner (𝐴3𝜔).


P1

P2

P3

P4

(a) Water jacket

P55

1 2 3 4 5

6 7 8 9 10

(b) Bolts and gasket

Figure 7: Schematic representation of the key parameters for water jacket and pretightening components.

Cylinder block/liner Cylinder head

Detailed model Simplified model Detailed model Simplified model

Figure 8: The parametric-oriented FE model of engine structure.

𝑃4: (eccentricity of the coolant inlet, initial value is

9mm) variations are considered to be within 45% ofits initial value,𝑃5: (length of the thread engagement, initial value is

30mm) this factor may vary from 20mm to 60mm,𝑃6: (pretightening sequence of the bolts, initial value

is Sequence 1) Sequence 1 is 3-8-9-4-7-2-10-5-6-1,Sequence 2 is 3-9-8-2-4-10-7-1-5-6, and Sequence 3 is3-8-2-9-4-7-1-10-5-6.

Due to the complex structural configuration and physicalboundary conditions, the distortion simulation based on theabove proposed FEmodel is a computationally intensive task.Moreover, the variation tendency of the dominant order ofdistortion is more desirable rather than a particular highlyaccurate calculation value during the parametric analysis. So,a simplified FE model is extracted from the previous detailedFE model by using feature suppression and deletion. Figure 8shows the parametric-oriented FEmodel of engine structure.With this newmodel, the finite element method can be easilyand economically be employed to deal with a large number ofcalculation steps.

Figures 9 and 10 provide details about the influence of thewater jacket and pretightening parameters on the dominantorder of distortion, respectively.

It can be seen that the thickness of the water jacket (𝑃1) is

a critical parameter concerning the 2nd order of distortion.At the beginning, as 𝑃

1increases, the distortion decreases

significantly, that is, primarily due to the positive effect of

the improvement of cooling conditions around the cylinderliner. However, when the thickness is larger than 9mm, theamplitude increases quickly, which indicates that the negativeeffect that follows with such increase of 𝑃

1also results in

weakening of the liner’s stiffness. Therefore, a compromisefor these two effects is necessary; that is, the thickness of9mm is optimal for 𝑃

1. In addition, the height of the coolant

inlet (𝑃3) also represents a considerable influence on the

resulting of the 2nd order of distortion. To acquire reasonableflow characteristic around the upper part of cylinder liner,the height of 55mm is preferred for 𝑃

3. In contrast, slight

distortion changes are observed for the other parameters (𝑃2

and𝑃4); according to the variation tendency, the diameter and

eccentricity of the coolant inlet should be selected as 28.8mmand 9mm, respectively.

As for the pretightening process, it is obvious that a longercylinder bolt (i.e., 60mm) and the 3rd-assembly sequenceshould be adopted since the applied pretightening forcewould be better distributed within the cylinder structure.Based on this, the parameter adjustment for water jacket andpretightening process design is made to implement the dis-tortion optimization, which is shown in Table 1. Table 2 liststhe comparison of dominant order of distortions between theoriginal and optimal design scheme. Figure 11 presents thecomparison of the flow characteristic and pretightening stressdistribution between the original and optimal design scheme.

In order to evaluate the improvement of the distortionlevel in optimal design, the problem of piston ring conforma-bility to distorted cylinder bore is further considered in this




Peak

val

ue o

f the

2nd

ord

er o

f

8101214161820222426

disto

rtio

n (𝜇

m)

Peak

val

ue o

f the

2nd

ord

er o

f

Peak

val

ue o

f the

2nd

ord

er o

fPe

ak v

alue

of t

he2

nd o

rder

of

10

11

12

13

14

15

16

17

18

disto

rtio

n (𝜇

m)

1011121314151617181920

disto

rtio

n (𝜇

m)

1011121314151617181920

disto

rtio

n (𝜇

m)

7 9 11 135The thickness of the water jacket P1 (mm)

35 45 55 6525The height of the coolant inlet P3 (mm)

7 9 11 135The eccentricity of the coolant inlet P4 (mm)

24.8 26.8 28.8 30.822.8The diameter of the coolant inlet P2 (mm)







Figure 9: Influence of the water jacket parameters on the peak value of the 2nd order of distortion.

3rd-assembly sequence2nd-assembly sequence1st-assembly sequence1st cylinder

2nd cylinder3rd cylinder4th cylinder

Peak

val

ue o

f the

4th

ord

er o

f

Peak

val

ue o

f the

4th

ord

er o

f

2

3

4

5

6

7

8

9

10

disto

rtio

n (𝜇

m)

3rd 4th2nd1stNumber of cylinder liners

30 40 50 6020The length of the cylinder bolt P5 (mm)

2

3

4

5

6

7

8

9

10

disto

rtio

n (𝜇

m)

Figure 10: Influence of the pretightening parameters on the peak value of the 4th order of distortion.

Table 1: The parameter adjustment for water jacket and pretightening process design.

Design parameters Water jacket Pretightening process𝑃1(mm) 𝑃

2(mm) 𝑃

3(mm) 𝑃

4(mm) 𝑃

5(mm) 𝑃

6(sequence)

Original 7 26.8 25 9 30 3-8-9-4-7-2-10-5-6-1Optimal 9 28.8 55 9 60 3-8-2-9-4-7-1-10-5-6


Table 2: The comparison of the dominant order of distortion between the original and optimal design scheme.

Maximum distortion (𝜇m) 1st cylinder 2nd cylinder 3rd cylinder 4th cylinder2nd order 4th order 2nd order 4th order 2nd order 4th order 2nd order 4th order

Original 15.35 6.54 14.86 5.99 14.95 6.03 15.75 6.64Optimal 11.83 3.18 11.52 2.89 11.67 2.93 12.09 3.29

Original design Optimal design

0

5547

.2

1109

4

1664

1

2218

8

2773

5

3328

2

3882

9

4437

6

4992

3

Convection_HeatTransfer_Coeff (W/m2 K) Convection_HeatTransfer_Coeff (W/m2 K)

Von mises stress (MPa) Von mises stress (MPa)

0.18

3

6.51

3

12.4

51

18.3

88

24.3

26

30.2

63

36.2

01

42.1

38

48.0

76

54.0

13

0.68

2

6.62

2

12.5

47

18.4

38

24.4

62

30.3

18

36.3

16

42.2

77

48.3

91

54.7

22

0

5858

.2

2343

2

2929

0

3514

8

4100

6

4686

4

5272

2

1171

6

1757

4

Figure 11: The comparison of the flow characteristic and pretightening stress distribution between the original and optimal design scheme.

paper: given FE data of cylinder liner distortions and a setof piston ring specifications, determine if the ring is fullyconformed to the distorted cylinder bore under actual engineoperation conditions. Till now, there are several bounds beingwidely adopted to estimate the piston ring conformability,namely, the analytically derived bounds (GOETZE bounds[9] and Dunaevsky bounds [11]), as well as the semiempiri-cally derived bounds (Tomanik bounds [26]). Critical valuesof cylinder liner distortions are established for analyzed pis-ton rings using either of the bounds [9, 11, 26] in this paper. Allthe parameters utilized in these bounds are deducible fromthe piston ring specifications. Figure 12 demonstrates thecomparison of different bounds for cylinder liner distortions.

By comparing the optimized distortion values listed inTable 2 with the critical values which are determined through

the above stated bounds, it can be found that a much bettersolution is obtained in the optimal design scheme, becausethe distortions in optimal design are minimized to satisfyboth the GOETZE and Dunaevsky bounds and approximatesto the tightest Tomanik bounds.

As a result of the reduction of cylinder liner distortions, abore profile closer to the perfectly circular cylinder liner isobtained. This provides an opportunity to further improvethe operational performance of the piston group. Since thepiston ring will achieve better sealing characteristics within alow distorted cylinder bore which leads to a reduction of boththe oil consumptions and exhaust emissions. Meanwhile,the requirement for the pretightening of piston rings alsodiminishes, which means that it may be possible to obtainlower engine friction losses and fuel consumptions.


Dunaevsky boundsGOETZE boundsTomanik bounds

Diametrical load (N)Height (mm)Thickness (mm)Nominal radius (mm)

15.261.463.72545.111600016.2212.16

81.09

3.242.43

Young’s modulus (N/mm2)

Upp

er li

mit

of th

e Fou

rier o

rder

of

disto

rtio

n (𝜇

m)

908070605040302010

0−10

3 4 5 6 7 82Distortion orders

Figure 12:The comparison of different bounds for cylinder liner dis-tortions.

5. Conclusions

This study is an initial attempt towards a computationalframework for the distortion optimization of engine cylinderliner. Some conclusions are extracted as follows:

(1) Detailed simulation based on the combination ofFEM and CFD is carried out to precisely capture therealistic distortions at any interest point of cylinderliner. Calculation results show that there are complexthree-dimensional distortions arising in the engineoperational process.

(2) The analysis methodology for spectrum characteriza-tion of bore distortions and various operational loadsis developed and implemented successfully in thisresearch.Theunique feature of thismethod is its capa-bility of distinguishing the relationship between thedominant order of distortion and special operationalload. Analytical results indicate that the 2nd- and 4th-Fourier orders are the dominant distortion orders.Moreover, the 2nd order of distortion is the mostsensitive to the thermal load (temperature patterns)and the mechanical load (pretightening stress) is themost critical to the 4th order of distortion.

(3) A parametric-oriented FE model is simplified fromthe previous detailed FE model by using feature sup-pression and deletion.The variation tendency of eachdominant order of distortion is obtained throughparametric analysis, and the optimal design schemefor water jacket and pretightening process is finallyachieved based on these findings. Simulation resultsindicate that a much better solution is obtained byusing this scheme.

Competing Interests

The authors declare that they have no competing interests.

Acknowledgments

The authors gratefully wish to acknowledge support byThe National Natural Science Foundation of China underGrant no. 51505383, The China Postdoctoral Science Foun-dation under Grant no. 2015M580874, andThe FundamentalResearch Funds for the Central Universities under Grant no.3102015ZY002.

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